sinxcos²ydx+cos²xdy=0，求此微分方程的通解

Question

如题所述

Answer 1

sinx(cosy)^2.dx+(cosx)^2.dy=0
-(cosy)^2.d(cosx)+(cosx)^2.dy=0
∫d(cosx)/(cosx)^2 = ∫dy/(cosy)^2
-1/cosx = -1/cosy + C'
1/cosx = 1/cosy + C本回答被网友采纳